Preparing student teachers to use computers in mathematics classrooms through a long-term pre-service course in Turkey

Recent studies have found short in-service teacher education programs are not providing adequate technology experiences to prepare their participants for teaching mathematics with computers. As an alternative to the short-term courses the author has been teaching a two-term mandatory undergraduate course within a mathematics teacher education program since 1995 to train student teachers and to investigate their perceptions on their preparation to use computers in their own teaching. This article describes issues that emerged from the analysis of this undergraduate course. Data were gathered through questionnaires and students' writings about the course activities. Findings indicated that computer literacy appeared to be an important key factor in utilising the course activities successfully. Students who felt prepared made the link between computer-based mathematical activities and school mathematics, and had more experience of using instructional software during the course than others. Findings of this nature can also assist teacher educators as they incorporate information technology into existing pre-service programs. The implications of these results for the designing and implementing of computer-based undergraduate courses and for further research in this field are discussed.     

Teaching problem-solving skills: A reflection on an in-service course for chemistry teachers in Singapore

A unit on the teaching of problem-solving skills, part of a chemistry inservice course for 25 experienced secondary school teachers in Singapore, presented two strategies: think-aloud and general problem-solving strategies. The evaluation of the unit was based on teachers' personal evaluations and their answers to a questionnaire which focussed on their responses and attitudes towards the teaching and learning of problem solving while using the two strategies. Specializations: problem solving and teaching and learning of science.     

The cognitive effects of a mathematics in-service workshop on elementary school teachers

Siegler's rule assessment methodology was used to investigate the cognitive effects of a 32 hour mathematics in-service workshop on 28 elementary shool teachers. This paper reports on attempts (a) to assess the levels of cognitive understanding of the basic concepts of proportion, probability, and correlation among elementary teachers, and (b) to change teachers' levels in understanding these concepts by a method of direct instruction. Significant improvements were noted in the levels of cognitive development associated with the concept of proportion. Though nonsignificant improvements were noted in the concepts of probability and correlation, all the teachers were assigned to the highest cognitive rule associated with the probability concept at the end of the workshop.     

Transactions between class teachers and student teachers

Interactions are explored between three pairs of class teachers and B.Ed student teachers on school experience in a traditional context. The main issues raised are the benefits of having students — expected and real — for the teacher, the features inherent in a successful class teacher/student teacher relationship and the implications of the research findings for the new partnership models of school experience. It is suggested that class teachers are prepared to invest expertise and time to support the students with the expectation of deriving benefits for their classes.     

A preliminary discourse analysis of constructivist-oriented mathematics instruction for a student with learning disabilities

Reform efforts in mathematics education arose, in part, in response to constructivist works on conceptual learning. However, little research has examined how students with learning disabilities (LD) respond to constructivist-oriented instruction in mathematics, particularly in moment-to-moment interactions. To understand the nature of constructivist-oriented mathematics instruction involving students with LD, the authors conducted a case study to analyze teacher–student interactions during constructivist-oriented small group instruction involving a student with LD. The student demonstrated, to a certain degree, the ability to reason mathematically when provided with appropriate opportunities and prompting. However, given the limited intervention time, his reasoning and problem solving did not seem to go beyond the semiconcrete level of operation, which may have inhibited his solving of complex word problems with large numbers. Findings indicate that more efforts are needed to support students, those with LD in particular, in their transitions from concrete or semiconcrete to abstract conceptual understanding and problem solving.     

Load reduction instruction in mathematics and English classrooms: A multilevel study of student and teacher reports

Load reduction instruction (LRI) is a practical instructional framework aimed at managing the cognitive demands experienced by students as they learn. LRI comprises five key instructional principles: (1) difficulty reduction during initial learning, as appropriate to students’ prior learning, (2) support and scaffolding, (3) structured practice, (4) feedback-feedforward, and (5) guided independent application. The present investigation explored student- and teacher-reports of LRI in both mathematics and English. The Load Reduction Instruction Scale – Short was administered to 1773 students and their teachers in 93 mathematics classrooms and 94 English classrooms. Multilevel (Level 1 student; Level 2 classroom) confirmatory factor analysis (MCFA) supported a Level 1 student LRI factor and a Level 2 class-average LRI factor in each of mathematics and English. However, two LRI factors emerged for teachers in each of mathematics and English: one factor related to Principle 1 (difficulty reduction) and one factor related to Principles 2–5 (scaffolding to autonomy). Follow-up multilevel structural equation modeling (MSEM) revealed that teachers adjusted their application of LRI Principle 1 (but not Principles 2–5) as a function of class-average prior learning (lower prior learning was associated with greater application of Principle 1). MCFA also showed that correlations between student- and teacher-reported LRI were low. Follow-up MSEM revealed that student- and teacher-reports of LRI uniquely predicted students’ effort and achievement—suggesting that students and teachers provide distinct insights into instruction (hence the low correlation between them) and highlighting the important role of both informants in capturing a comprehensive perspective on instruction in the classroom.     

Convergence of observer ratings and student perceptions of reform practices in sixth-grade mathematics classrooms

As part of a research project examining relationships between instructional practices and student cognitive and social outcomes in middle-school mathematics classes, external observers and students reported perceptions of teachers’ instructional practices. The extent to which students in classrooms identified by external raters as reform-oriented actually perceive instruction in ways aligned with reform principles has not been established. A 25-item observation protocol aligned with the reform practices called for in the Standards of the National Council of Teachers of Mathematics (NCTM) was used to develop a quantitative profile of instructional practices across two lessons in each of 28 classes of 15 participating teachers. Students in each of the observed classes completed a 49-item survey of their perceptions of instructional practices. As items for both the observation protocol and Student Survey were designed to measure alignment with the same dimensions of reform practice, the convergence of these two data sets was examined as a means to confirm the observation ratings. The findings show moderately strong correlations between ratings of external observers and perceptions of sixth-grade students across three dimensions (pedagogy, tasks and mathematical interactions) of reform-oriented teacher practice in mathematics classrooms. Implications of these findings for future research are discussed. The research in this article was supported by the National Science Foundation (NSF) under grant REC 0125868. The opinions expressed here are those of the authors and do not necessarily reflect the view of NSF. The research was also supported by the Roysters’ Fellowship to Mark Ellis from the Graduate School at the University of North Carolina at Chapel Hill.     

Examining the supervision of mathematics student teachers through analysis of conference communications

Student teaching is often a capstone experience in the preparation of mathematics teachers. Thus, it is essential to better understand key aspects of the experience. We conducted a qualitative study of post-lesson conferences led by supervisors (classroom cooperating teachers and a university supervisor) working with mathematics student teachers. Analysis of conference communications revealed differences in the types and content of communications in conferences led by the cooperating teachers and by the university supervisor. Cooperating teachers tended toward evaluative supervision that lacked a focus on the mathematics of the lessons while the university supervisor tended toward educative supervision, guiding student teachers to reflect on and learn from their own classroom experiences including the mathematics of their lessons. Differences are discussed, and suggestions concerning the supervision of student teachers are made along with recommendations for further research.     

论师生话语权的共享

长期以来，在师生交往中师生话语权处于失衡状态，主要表现为教师话语的膨胀与学生话语的失落。让师生共享话语权的关键在于唤醒学生的主体意识，通过对话使师生共享话语权力。     

A comparison of student thinking in a mathematics and a science classroom

Conclusion This study represents the second phase of a major research project. Much of the data has confirmed what emerged in the first phase (Marland & Edwards, 1982), particularly the idiosyncratic nature of student functioning and the complexity of the teaching/learning process. In the mathematics and science classrooms studies it appeared that neither was more coercive of student attention or lesson-relevant thinking. However the maths lessons elicited more conscious application of learning processes and more involvement in wider classroom activities, particularly responding to teacher questions. The science lessons involved more interaction with the neighbour and a much greater variety of student mental and physical activity. The Grade 8 students in this study, when compared with the Grade 10 and 11 students from phase one, were much more straightforward in their reactions and interactions, and were much more compliant. The complex deception strategies and involved interpretations and attributions so prevalent with the more senior students were almost completely absent with the Grade 8 students. The size of difference was an unexpected result and appears a fascinating area for future research.     

Contribution of mathematics in-service training course to the professional development of elementary school teachers in Israel

The present study aimed to explore the contribution of a mathematics in-service training course to elementary school teachers (1st–6th grades) in Israel. The study was conducted among 449 educators. They were required to respond to background questions. Moreover, they were asked to indicate their expectations from the in-service training course and, at its end, point out to what extent they benefitted from that course. The research findings illustrate that educators who teach mathematics at elementary school and attended the course are generally women in their 40s, holding a BEd degree and a teaching certificate not in mathematics, with an average 13-year seniority. The participating teachers indicated their wish to enrich their didactic knowledge in order to acquire varied tools for teaching mathematics to the entire pupil population as well as to gifted pupils and pupils with learning difficulties. Nevertheless, their demand to expand their mathematics knowledge was very limited. Based on the fact that most teachers have no mathematics education, this is a surprising finding as, in order to be a good teacher, one must be versed not only in Pedagogical Content Knowledge but also in Subject Matter Knowledge.     

Constructing competence: an analysis of student participation in the activity systems of mathematics classrooms

This paper investigates the construction of systems of competence in two middle school mathematics classrooms. Drawing on analyses of discourse from videotaped classroom sessions, this paper documents the ways that agency and accountability were distributed in the classrooms through interactions between the teachers and students as they worked on mathematical content. In doing so, we problematize the assumption that competencies are simply attributes of individuals that can be externally defined. Instead, we propose a concept of individual competence as an attribute of a person's participation in an activity system such as a classroom. In this perspective, what counts as “competent” gets constructed in particular classrooms, and can therefore look very different from setting to setting. The implications of the ways that competence can be defined are discussed in terms of future research and equitable learning outcomes.

Expectations of higher education students: a comparison between the perception of student and teachers

Higher education institutions are ever more interested in the development of tools that enable them to evaluate and manage the expectations of their students with the purpose of attracting and keeping them satisfied. This research compares what the faculty believes the students expect from a higher education institution with the expectations of students entering higher education. A quantitative study was performed with students from a higher education institution through the application of a questionnaire covering 32 different expectations. The perceptions of the faculty were also collected through the same questionnaire, suitably adapted. The results of the investigation demonstrated differences in thinking between students and professors, with 19 variables representing student expectations that showed statistically significant mean differences. In 13 variables the students had greater expectations than the faculty believed, while for six variables the faculty indicated higher expectations than the students declared. Identifying the existence of this gap in knowledge will allow the higher education institution to adjust its services to the expectations of students, leading them to greater satisfaction.     

Professional growth during cyber collaboration between pre-service and in-service teachers

This study investigates the potential for two-way professional development during a telecollaboration between pre-service and in-service teachers (PSTs and ISTs), exemplified with the context of TESOL (Teaching English to Speakers of Other Languages) MA program. Thirteen IST-PST dyads engaged in collaboration with e-pals and completed two tasks: professional interviews and lesson planning. Thematic analysis was used to analyze questionnaire responses and work logs. Partakers all exhibited the cultivation of reflective thinking by sharing knowledge and learning experiences—occupationally, pedagogically, and academically—with each other. The study depicts a need-based and task-based collaboration mechanism in a cyber professional community; mutual benefit was achieved with minimum social pressure.     

A cross-cultural comparison of German and Canadian student teachers’ assessment competence

ABSTRACT

Teachers’ competence in educational assessment is a key feature in teacher professionalism. Understanding of assessment competence has evolved from the learning of technical skills in assessment to a context-dependent, socially defined understanding encompassing a multitude of approaches to assessment. Thus, a holistic approach to assessment competence is used in this research to specifically consider the role of education culture on assessment competence. In particular, we compared Canadian and German student teachers with regard to their self-rated competence in, and approaches towards, educational assessment. While structural analysis revealed that the overall dimensions in which assessment is perceived do not depend on culture, ANOVAs pointed at some differences between the two countries, particularly concerning assessment purposes and approaches to fairness.     

Teacher noticing and its growth toward expertise: an expert–novice comparison with pre-service and in-service secondary mathematics teachers

Educational Studies in Mathematics - Mathematical modelling competencies have become a prominent construct in research on the teaching and learning of mathematical modelling and its applications in...     

Studying new forms of participation and identity in mathematics classrooms with integrated communication and representational infrastructures

Wireless networks are fast becoming ubiquitous in all aspects of society and the world economy. We describe a method for studying the impacts of combining such technology with dynamic, representationally-rich mathematics software, particularly on participation, expression and projection of identity from a local to a public, shared workspace. We describe the types of mathematical activities that can utilize such unique combinations of technologies. We outline specific discourse analytic methods for measuring participation and methodologies for incorporating measures of identity and participation into impact studies.

The juxtaposition of instructor and student perspectives on mathematics courses for elementary teachers

This qualitative study examined perspectives of two key stakeholder groups, instructors and students, on mathematics content courses for prospective elementary teachers (Mathematics for Teachers [MFT] courses). A collective case study approach, which drew from the data of two cases in different but comparable settings, contributed to the robustness of the findings. Cross-case analysis of the interview data revealed several convergent themes: the role of affect in student learning, pedagogy and instructor disposition, connections to the elementary classroom, and mathematics content. The findings included both conflicting and complementary perspectives between the two key stakeholder groups. When juxtaposed, the multiple viewpoints offer insights into some of the central issues related to teaching and learning in MFT courses and suggest potential avenues for improving experiences in these courses.     

Teacher enthusiasm and self-efficacy,student-perceived mastery goal orientation,and student motivation in mathematics classrooms

The purpose of this study is to examine whether teacher enthusiasm and classroom management self-efficacy are related to classroom mastery orientation and student motivation. We used data from 803 students in grades 9 and 10 (53.3% girls) and their mathematics teachers (N = 41; 58.5% men). Student-perceived teacher enthusiasm was related to classroom mastery orientation as well as to intrinsic value and cost at the student level. Teacher-reported self-efficacy was related to classroom mastery orientation at the classroom level. At both the individual and the classroom level, classroom mastery orientation was related to attainment and utility value.     

A discourse analysis of collaboration between academic and student affairs in community colleges

The purpose of this study was to understand the nature of collaboration between academic affairs and student affairs units in the community college context from a qualitative perspective. A discourse analysis study was conducted to explore the ways in which collaborative practice was discussed and understood by chief and midlevel academic and student affairs practitioners in three different community college settings. By using their actual practice and desired practice to understand collaboration in this setting, this article offers a definition for academic and student affairs collaboration that has been absent from most literature on the topic.